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Chemometrics has different applications in electrochemical analyses, such as experimental design and optimization, data treatments, sample classification, calibration for determination of concentrations and model identification. In general, over the past two decades, instrumentation has been significantly developed. This is especially the case for electrochemical instruments. Such progress has provided increasing opportunities for the application of chemometrics in electrochemical analyses. Developing an electrochemical technique by chemometric methods may supply a valuable resource for accurate analyte quantification when the absolute separation is not accomplished, or unexpected components are present in the sample being analysed.

The input quantities of our primary interest, i. Therefore, in this chapter, calibration means the operation of relating instrumental signals to analyte concentrations. In analytical chemistry, univariate calibration employs a calibration curve as a general method for the determination of the concentration of a constituent in an unknown sample [ 26 ]. A more general calibration process involves the relationship between the concentrations of various constituents in a test sample and multiple measured responses, i.

In contrast to univariate calibration, which works with a single instrumental response measured for each experimental sample, multivariate calibration works with many different signals for each sample. Depending on the instrumental setup, the delivered data for a single sample may have different degrees of complexity. The simplest multivariate data are those produced in vector form, i. Multivariate calibration using vectorial data has given rise to a highly fruitful analytical field that today is routine in many industrial laboratories and process control units [ 28 ].

Multiple analytes can be determined simultaneously in the presence of others, possibly unknown constituents, provided they have been properly taken into account during the calibration phase [ 29 , 1 ].

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One is the increase in sensitivity, because the measurement of redundant data tends to decrease the relative impact of the noise in the signal. Selectivity does also increase, because each new instrumental mode, which is added to the data, contributes positively to the overall selectivity. The list may continue with data arrays with additional modes per sample [ 26 ]. On the other hand, with data for a group of samples it is possible to create an array having an additional mode, the sample mode. On the basis of above fact, an alternative nomenclature has been developed, in which calibrations are named according to the number of ways modes of an array for a sample set.

Top: Data for a single sample. Bottom: Data for a set of samples [26]. The column vector an is collected in the scores matrix A , whereas vectors bn and cn are collected in the loading matrices B and C usually bn and cn are normalized to unit length.

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A requirement for quadrilinearity of a data array for a sample set is that the three instrumental profiles for each constituent are equal for all samples [ 26 ]. The theory behind the proposed procedure will be briefly discussed.

The current signal intensity in DPV can be obtained using the following equations [ 61 ]:. Linearity is a property assumed by multivariate linear calibration algorithms. However, in many electroanalytical situations, slight deviations from linearity could be observed such as in the presence of interactions among components. Such problems become more complicated when signals are overlapping.

The data alignment is based on digitally moving a voltammogram towards a reference voltammogram, with certain objective function such as correlation coefficient, residual fit, similarity index, etc. The most algorithms used for data alignment require a reference voltammogram, to which all the remaining ones are aligned. Suboptimal choice of the template could affect the alignment results [ 63 ]. The most frequently used alignment algorithms are correlation optimized warping COW [ 64 ], interval correlation optimised shifting icoshift [ 65 ], Gaussian peak adjustment GPA [ 66 ], Gaussian peak adjustment with transversal constraints GPA2D [ 67 ], asymmetric logistic peak adjustment ALPA [ 68 ], shiftfit [ 69 , 70 ] and pHfit [ 71 ].

For understanding a detailed description about the mathematical aspects of COW algorithm the reader is referred to Ref. For understanding a detailed description about the mathematical aspects of icoshift algorithm the reader is referred to Ref. The shiftfit corrects the data matrix from the signal movements and for this purpose, it optimises by least squares of the potential shift of every pure voltammogram with respect to a reference position.

To correct the potential shift, there are peakmaker , shiftcalc and shiftfit functions. Peakmaker generates a Gaussian peak as an initial estimation of the pure voltammograms. The pHfit algorithm can solve more intricate systems like those encountered in voltammetric pH titrations by imposing a shape restriction to the movements of the signals as a function of potential, by means of adjustable sigmoid or linear functions [ 71 ].

After shiftfit and pHfit , the GPA algorithm based on a new strategy, parametric signal fitting PSF , was proposed for the chemometric analysis of voltammetric data when the pure signals do not maintain a constant shape [ 66 ]. This is based on the fitting of parametric functions to reproduce the shape of the signals. Such parameters determine not only the height and position of the signals as in the algorithms above but also the width at both sides of the maximum. In the proposed method, the use of two separated Gaussian functions at both sides of the maximum sharing the same height and position but different widths is a new and simple solution for the fitting of asymmetric peaks.

A new method, GPA2D, was developed as a significant improvement of the GPA which includes, for the first time, transversal constraints to increase the consistency of the resolution along the different signals of a voltammetric dataset [ 67 ]. The aim of GPA2D is to extract a physicochemical sense to the evolution of the signals and their shifts along the experimental axis.

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  8. Baseline correction has been considered as a critical step for enhancing the signals and reducing the complexity of the analytical data [ 72 , 73 ]. Considering this aim, Eilers et al. Details of the implementation of the mentioned method can be found in the literature [ 74 , 75 ]. Applications of different multivariate analysis techniques as applied to electroanalytical data.

    In an interesting work, Kooshki et al. Finally, they assessed the analytical utility of the proposed method by applying it to the determination of Trp in a fresh meat sample. The accumulation time t acc was chosen as the third variable third way. The t acc was varied in 5 s intervals and with the aim of increasing the total t acc value without electrode saturation, the equilibration time was fixed at 5 s, and t acc was varied from 5 to 25 s, thus five voltammograms for each sample were recorded. Finally, the proposed method was used to the analysis of river water samples as real cases and the results were encouraging.

    Applications of Chemometrics‐Assisted Voltammetric Analysis

    A linear dependency exists in the pulse duration profiles of the electroactive species in the mixture samples. Rank deficiency of the mixture data matrix was broken by matrix augmentation. So, this shift was corrected with shiftfit program. Khoobi et al. Finally, the developed method was successfully applied to simultaneous determination of Bet and Ate in human plasma. In an interesting work by Khoobi et al.

    The CCRD was employed to generate an experimental programme to model the effects of different parameters on voltammetric responses and the RSM was applied to show the individual and interactive effects of variables on the responses. Finally, by the developed methodology, satisfactory results were obtained for the determination of DA in the presence of EP in spiked human blood plasma samples.

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    Ghoreishi et al. Finally, the method was applied for simultaneous determination of SMT and SPY in spiked human serum and urine samples. Masoum et al. The solution to the problem of rank deficiency was the combined analysis of the rank deficient matrix with other matrices in the column direction that can have the suitable information to detect the presence of the hidden components [ ]. Finally, the application of the proposed method was examined for simultaneous determination of SMX and SMT in human blood serum and urine samples.

    Jalalvand et al. Mora Diez et al. As can be appreciated there exists a high degree of overlapping among analyte and interferents signals. The areas under the kinetic profiles were used to build a calibration curve that allowed them to obtain the concentration of ethiofencarb in the validation samples. A Voltammograms corresponding to validation sample number 1, before and after background correction.

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